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Simplifying 12a3 + -5a2 + -25a = 0 Reorder the terms: -25a + -5a2 + 12a3 = 0 Solving -25a + -5a2 + 12a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-25 + -5a + 12a2) = 0 Factor a trinomial. a((-5 + -4a)(5 + -3a)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-5 + -4a)' equal to zero and attempt to solve: Simplifying -5 + -4a = 0 Solving -5 + -4a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -4a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4a = 0 + 5 -4a = 0 + 5 Combine like terms: 0 + 5 = 5 -4a = 5 Divide each side by '-4'. a = -1.25 Simplifying a = -1.25Subproblem 3
Set the factor '(5 + -3a)' equal to zero and attempt to solve: Simplifying 5 + -3a = 0 Solving 5 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3a = 0 + -5 -3a = 0 + -5 Combine like terms: 0 + -5 = -5 -3a = -5 Divide each side by '-3'. a = 1.666666667 Simplifying a = 1.666666667Solution
a = {0, -1.25, 1.666666667}
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